Solutions to Problem Set #2 Exercises on Chapter 6

ECO05: Labor Economics Instructor: Michael Rizzo Solutions to Problem Set #2 Exercises on Chapter 6 Distributed: Wednesday, November 2 nd, 2005 Due: Friday, November 11 th, 2005 solutions will be posted on website after class that day. If you had much difficulty and the posted solutions don t clear them up, be sure to see me! For all of the following, assume people sleep hours a day and allocate 16 hours per day for leisure, work and work-related activities. (1) Draw the budget line if the non-labor income equals $100 and wage equals $10 per hour. What is the opportunity cost of choosing one more hour of leisure? Answer: The budget line is simply one with a slope of $10 and an amount of income of $100 at 0 hours of work (see below). Money per Day ($) $260 Budget Constraint with Nonlabor Wage = $10/hr, Nonlabor = $100 $100 M = nonlabor income = 0 16 12 12 Hours of LEISURE per Day The opportunity cost of choosing one more hour of leisure is simply the wage rate this is what I give-up if I stay out of work for one more hour. (2) Draw both the budget line and indifference curve showing a situation where an individual chooses not to work. This is known as a corner solution - NOTE: the solution does not involve a tangency point as it did previously in what are known as interior solutions. Answer: Note that the indifference curve touches the budget constraint at the point

of zero hours of work. This would be true regardless of how much income a person had at this point. Money per Day ($) $160 Indifference Curves and Budget Constraint Wage = $10/hr, Nonlabor = Individual has a preference for LEISURE $90 0 16 12 12 Hours of LEISURE per Day (3) Using indifference curves and budget lines, show that a wage increase may induce an individual to supply less hours to the labor market. Which effect dominates in this case? Answer: When wages increase and a person enjoys more leisure, we know that the income effect has dominated. Why? When wages increase I can still work the same amount of hours and have more income! I am better off. When I have more money in my pocket, I purchase more of the goods that I like, among these are leisure time. So the income effect says to buy more leisure (work less). The substitution effect tells me that since the wage increases, what I stand to lose by staying home for another hour is greater than before all else constant I will choose to work more hours as leisure is relatively more expensive after the wage change. 2

Money per Day ($) B A 0 16 12 12 Hours of LEISURE per Day () You just won the lottery. What does the income effect say will happen to your hours of work? The substitution effect? Explain your reasoning clearly and concisely. Answer: Winning the lottery generates a pure income effect. By definition, the income effect tells us that a person buys more leisure hours when she is given more income, holding wages and preferences constant. Since she wins the lottery, she is made better off and will thus buy more leisure. The relative price of leisure is unchanged here however. Taking off from work for one extra hour does not result in a loss any different than before the lottery win, so there is not a substitution effect in this example. (5) Draw an indifference curve for a person that requires money income and leisure hours in fixed proportions (e.g. for every hour of leisure she enjoys, she needs $50 of income no more, no less). Answer: In class we saw that such preferences describe goods that are perfect complements. Intuitively, I am only happy when I have an exact amount of each good in fixed proportions. Suppose I love to camp and that I need two full days off to go camping. Each weekend of camping costs me $100 of traveling and food expenses. Once I get into the woods, money is useless to me, all I need is the time to enjoy myself. In this case, my preferences for money and camping time are in fixed proportions I require 2 days of free time for every $100 I have. If I only have two days of free time to go camping, giving me more money once I am in the woods is utterly useless (can I buy a tree?). Similarly, if you give me weekends of free time to go camping, but only leave me with $100, then I can only use one of those weekends, so the additional time is useless. You will see that these indifference curves are perfectly L-shaped and that a labor supply equilibrium will occur at the elbows. These preferences are referred to as Leontief preferences. 3

Money per Day ($) 0 Indifference Curves - Leisure and Perfect Complements $700 $600 slope = $50/hour of leisure = exact degree of complementarity $500 0 $300 $200 $100 0 16 12 12 Hours of LEISURE per Day (6) If I tell you that there is a wage change and we see workers working fewer hours, are worker indifference curves likely to be steep or flat? Is the income or substitution effect of this wage change on labor supply larger? Why? Explain in words. Answer: People with steep indifference curves (or that are located along steep portions of their indifference curves) are those that are likely to work less when wages change. These people value leisure much more than they do income. To maximize their utility, they seek to purchase as much leisure as possible given their income constraints. Thus, when wages rise, it must be the case that the income effect (work less) dominates the substitution effect (work more). They will use a small amount of this wage increase to enjoy more income, but will use an even larger portion to buy more leisure. Their utility will be larger than initially when wages increase. When wages fall, it must be the case that the substitution effect outweighs the income effect for these same people. Why? These folks prefer leisure when wages fall, the cost to these people of missing an hour of work has fallen, so the substitution effect says to consume more leisure. The income effect says to increase work hours. Since I said that people work fewer hours, it must be the case that the substitution effect dominates. In this case, the wage decrease results in a loss of utility. It is still possible that indifference curves are flat we know that the income effect of a wage increase is larger the more hours a person works so we may in fact have someone with a taste for income nonetheless working fewer hours.

(7) Suppose that the government is considering several options to guarantee that legal services are provided to the poor. Analyze the work incentives of each of these programs. Answer: See Chapter 6, Review Question #3. Graphs and Answers are in back of book. Some additional comments: (a) All lawyers would be required to devote 5% of their work time to the poor free of charge. This is equivalent to a wage decrease. We know that labor supply impacts of wage changes are ambiguous they depend on the relative size of the income and substitution effects. Coincidentally, it can be argued that lawyers have flat indifference curves, so we might expect the income effect to dominate for them (work more). (b) All lawyers would be required to provide 100 hours of work, free of charge, to the poor. This is equivalent to a loss of nonlabor income that generates a pure income effect. Why? Think of a lawyer spending 2,000 hours per year in the office at a wage of $50 per hour. Given this work effort, she has $100,000 per year in earnings. Now the government says that the forst 100 hours of her time each year must be provided free of charge to the poor. After this program, for a similar work effort of 2,000 hours, she is only paid for 1,900 hours totalling $95,000 in income. Since she is worse off, she buys less of all goods, including leisure so the income effect says to work more. Incidentally, this change does not result in the opportunity cost of leisure changing. If she works one less hour now, she still only stands to lose $50, so there is no substitution effect. Or is there? If there are lawyers working around 100 hours per year (is this realistic, I think not), then what is the cost to them from staying home from work an extra hour? Is it $50? No, it is ZERO. Since I work for free, then by staying home I do not stand to lose anything. In this case there is an enormous substitution effect driving these folks out of the labor force due to the net wage rate of zero (ask yourself, would you prefer of income with 2 hours per day of work, or would you prefer of income with 0 hours per day of work?). (c) All lawyers who earn more than $50,000 in a year would have to donate $5,000 a year to a fund that the government would set up to hire lawyers (at market wages) for the poor. This causes a loss of nonlabor income, but only after the threshold is reached. This program does not affect workers making below $50,000 per year. This program has a pure income effect only for people earning much more than $50,000 per year (leading to more work hours). However, for 5

folks making near $50,000 per year, it might be the case that this $5,000 tax causes a reduction in work hours until they make exactly $50,000. Why? This tax, although it doesn t affect the market wage rate, creates an effective negative wage rate for folks making near $50,000 we may see people reduce work hours in order to avoid the tax. This is a huge substitution effect to see why, consider a person initially making $51,000 per year. When this program is implemented, she loses $5,000, leaving her with $6,000 in net income. Now, we see that what she stands to lose by working fewer hours such that her pretax income is $50,000 is NEGATIVE! If she works only enough to make $50,000, then her take home income has increased from $6,000 to $50,000 she is getting paid $,000 to stay home. Since she is being paid to enjoy leisure time, she will most certainly take that time off. () Suppose we have no non-labor income. However, we have a wage offer of $20 per hour. (a) Draw the budget constraint. Now, suppose we have $50 per day of nonlabor income as well, (b) draw the new budget constraint. Now, suppose that in order to work we must pay for child care. This cost is not fixed, clearly the more hours I work, the more hours I must keep my child in child-care. Assuming the child-care market is competitive, if it costs me $10/hour for child-care, (c) redraw my budget constraint (ignore any time costs or other transportation costs). Answer: See below. The childcare cost can simply be thought of as a decrease in the wage rate. For those mothers initially not in the labor force, the presence of childcare costs serve to reduce the probability of her entering the labor force because her net wage after child-care costs is far smaller than her reservation wage. For those that are already in the market, the impact on labor supply is ambiguous, though there has been some empirical evidence suggesting that the substitution effect is larger than the income effect. 6

Money per Day ($) Budget Constraint with Nonlabor Wage = $20/hr, Nonlabor = $50, $10 childcare cost $370 $320 $210 (c) (b) $50 (a) M = nonlabor income = $50 0 16 12 12 Hours of LEISURE per Day (9) Let s consider two different methods of paying child support. Suppose before divorcing, a father has $50 of non-labor income and a wage of $20 per hour. Now, suppose he is divorced and must pay per day in child support. Draw his new budget constraint. What are the work incentive effects of this mandated support? Suppose instead that he were able to keep all of his non-labor income, but that every dollar per day he earns in the market would be paid in alimony until a total of per day is awarded. Draw this budget constraint. What are the work incentive effects of this mandated support. Compare the impacts of the two programs. Answer: The first program is equivalent to decrease in non-labor income of per day. For men that are currently working, this results in a pure income effect that increases work effort. For men not currently working, work incentives are not likely to chang as neither the market wage rate nor the reservation wage changes. The second program is one that results in a net wage rate of zero on the first two hours of work, after which the wage rate returns to the market wage rate. The husband always keeps his nonlabor income. So, if he works zero hours, he ll have $50. If he works one hour, he can earn $20 in wages, but must in turn give that to his wife he is still left with $50. If he works 2 hours, he can earn, but must pay all to his wife, leaving him still with $50. If he works 3 hours, he can earn $60, but must pay his wife, leaving him with $20 of earnings and $50 of 7

nonlabor income totalling $70. Beyond here, he can keep all incremental wages, so we see a kink at 2 hours of work and a slope equal to the wage beyond that point. For those currently not working, the work incentives have been decreased due to an increase in the reservation wage (if I don t work, I don t pay alimony!). For those that are currently working, there are two cases to consider. First, for those working many hours, the work incentives are increased due to the pure income effect generated by the alimony payment. For those with very steep preferences and/or working few hours initially, there might be an incentive to drop out of the labor force. For these people, the net wage rate of zero on the first two hours of work generates a HUGE substitution effect that might induce them to supply no hours to the market (Why? If I work one hour initially, by quitting I lose $20. If I work one hour after the program in initiated, then by quitting I lose. Would you prefer to work for no money or would you prefer to stay home with no money?) Certainly for any folks working less than 2 hours per day, they will have more utlitity by dropping out. Even some folks working more than 2 hours will be able to achieve higher utility by dropping out of the labor force. Clearly, the second program introduces more serious negative work incentives than the first program does. Not only does the second program introduce perverse work incentives, but it also introduces the possibility that alimony payments will not be made. Money per Day ($) 2 methods of paying alimony Wage = $20/hr, Nonlabor = $50 per day alimony payment $370 $330 $210 before alimony $50 0 16 after alimony 12 12 Hours of LEISURE per Day M = nonlabor income = $50

Money per Day ($) $370 2 methods of paying alimony Wage = $20/hr, Nonlabor = $50 alimony payment - each dollar of income awarded to spouse until reached $330 $210 before alimony $50 after alimony 16 12 M = nonlabor income = $50 0 12 Hours of LEISURE per Day (10) The first year of graduate school is incredibly intense for Economics PhD studentsthey take many classes with continuous exams, study day and night, learn more math than anyone ever should, and watch their social life dwindle. At the end of the year, they face a series of qualifying exams that must be passed to continue their studies. The torture ends in mid-june and the students are expected to return in mid-august for another intense but more reasonable year of work. For some students, the Department offers a Fellowship that gives them what is equivalent to $60 per work day over the summer. However, if the graduate student takes a job with an outside firm during this two month period, the amount of the Fellowship is reduced dollar for dollar (in other words if the student were to make $200 over the summer, they would get $200 less in the Fellowship.) Assume that the student could make $15/hr at a summer job. Draw the budget constraint for the graduate student. Show the optimal choice for a student who is really tired of working. Answer: 1 and 2 shown on diagram below. Note: The steep nature of the indifference curve suggests that the individual needs a rather large amount of money to give up even a little bit of leisure and be as happy. Given the incentives structure in the budget constraint, however, even those with more standard indifference curves will choose the no work option frequently. You can try to draw some other indifference curves on your own to see.} 9

Money 20 U=U** 60 0 12 16 Hours of Leisure 16 0 Hours of Work Would a graduate student ever work 3 hours a day? Explain. A graduate student will never work 3 hours a day because he/she can have the same amount of money AND 3 more hours of leisure if they choose not to work. Suppose you are a student that receives $60 from Cornell. If you worked 2 hours, how much money would you receive from your employer? How much do you have to give back to Cornell? So how much money did you keep from Cornell? How much monetary income do you have? If I work 2 hours, I receive $30 from the employer. I return $30 to Cornell, keeping $30 that Cornell gave me. I have $60 a day. If you work the third hour, how much more money will you get from the employer? How much more money would you have to give back to Cornell? How much is your net gain in monetary income from working the third hour? What is the slope of the budget constraint at these wages? Is this a coincidence? If I work a 3rd hour, I will get another $15 from the employer. I will give back another $15 to Cornell. My net gain from working the third hour is. The slope of the budget constraint in this region is 0. This is not a coincidence. The budget constraint tells me the maximum amount of money I can have if I take a given amount of leisure. So the slope equals the change in y (the amount of monetary income) for a 1 unit change in x (the amount of leisure). I give up the net gain in monetary income from working the next hour to enjoy one more hour of leisure. 10

If you were working 6 hours, you would earn $90 from the firm and you would have to return all $60 you received from Cornell. How much would monetary income would you have? If you worked one more hour (7 total) how much monetary income would you have? What is the marginal benefit of working the 7 th hour? What is the slope of the budget constraint? If I worked 6 hours, I would have $90 in monetary income. I would have $105 if I worked one more hour (7 hours total). The marginal benefit of the 7th hour is $15. The slope (absolute value) of the budget constraint in this region is 15. What sort of behavior is the Department encouraging? By implementing this fellowship system, the Department is encouraging students to relax over summer (Note that I am including the possibility of starting research projects under leisure activities). This may be to help ensure that their TAs are less stressed and much friendlier than they would otherwise be. (11) Compare the labor force participation rates for high school dropouts, high school graduates, workers with some college, and college graduates for September 2005. http://www.bls.gov/news.release/empsit.t0.htm (12) Find me one piece of labor market data that indicates the economy is not doing so well. Why did you choose this? (13) Find me one piece of labor market data that indicates the economy is doing well. Why did you choose this? (1) One argument opponents of Wal-Mart often make is that Wal-Mart free rides on government welfare payments in that welfare payments enable Wal- Mart to pay lower wages. (a) According to the theory of labor supply we are learning, what must be the labor market impact of welfare programs according to this story? How does this story square with the theory you are learning and the empirical evidence on the employment effects of welfare? Simply speaking, the critics are stating that the supply of labor to Wal-Mart shifts to the right which lowers the wage workers receive and enables more 11

workers to be hired. The theory of labor supply tells us that welfare programs typically generate income and substitution effects that in most cases work to indicate that workers will reduce work effort, or have an ambiguous prediction on work effort. Furthermore, the empirical evidence suggests that there are modest reductions in labor supply when welfare-like programs are enacted. In other words, it is highly doubtful that labor supply increases when workers are given cash grants from the government. (b) Opponents claims against Wal-Mart go something like this: absent welfare payments, workers need and therefore demand and get paid from Wal-Mart higher wages. In other words the supply of labor to Wal-Mart would be lower in the absence of welfare payments. What two factors MUST be true in order for workers to bid up their wages in the absence of welfare payments? Suppose the average wage paid to Walmart workers when welfare is in place is $7.00 (it is actually higher than this). In order for workers to get paid a wage of say, $15.00 without welfare payments, then it must be the case that these workers are more productive than they are currently. Since Wal-mart aims to maximize profits, then they would not pay $15.00 if this is not what workers were able to generate in revenues for them. Second, it must be the case that workers in the absence of welfare payments have the opportunity to work elsewhere if Wal-Mart is in fact exploiting them (i.e. paying them below their productivity). (c) Therefore, for the claims of Wal-Mart opponents to be true, based on what you answered in part (b), what MUST be true about the impacts of welfare payments on potential Wal-Mart employees? It must be the case that receiving welfare payments reduces worker ability to earn $15 per hour. How would this happen? First, it might be the case that receiving welfare payments makes workers LESS productive. If this does in fact happen, does Wal-Mart benefit from it? I think not, since both wages and productivity will fall. Second, one would have to argue that welfare payments reduce the competition for Wal-Mart s employees by other companies. Perhaps this might be true in the long run if government financed welfare programs increase employer costs enough to drive firms out of business, but highly unlikely in the short run. (d) Suppose now that neither of the events you describe in part c actually occurs. Provide one possible explanation for why the presence of welfare payments results in low-skilled workers earning LESS at Wal-Mart (this may in fact be the only explanation). Well, if welfare payments do not reduce productivity and do not reduce competition for workers, the only thing that must be happening is that workers 12

that receive welfare no longer WANT to earn $15.00 per hour from Wal-Mart. This is insane. This logic is likely a result of the common thinking that market transactions are based on people s needs rather than their wants. The critics likely believe that welfare payments reduce the amount of money that welfare recipients need to get by, so welfare recipients are now willing to work for wages less than they would demand absent welfare payments. The intuition just doesn t make sense. Furthermore, if workers treat these welfare payments as pure nonlabor income then we know that the presence of welfare payments results in an INCREASE in worker reservation wages and reservation hours of work. Of all of the silliness I have read about Wal-Mart, this might take the cake. 13